^^kO^'" ^ ^ « V 



-^ v^ ^;^; 



V o ^ . 



Electrical '. . . 



Measurements 



FOR 



AMATEURS 



BY EDWARD TREVERT. 



I ILLUSTRATED . -^ 

APRiO 1894 .) 



-^Of WA8H\*^^ 



1894. 
BUBIER PUBLISHING COMPANY 

LYNN, MASS. 



/s-^v^X 



^-• 



COPYRIGHTED BY 

BUBIER PUBLISHING COMPANY, 

LYNN, MASS. 

1894. 



PfJEFAGE. 



It frequently happens that persons experimenting 
with electricity and electrical apparatus, have need of 
making measurements of the different factors con- 
cerned.^ 

For those who are working on a small scale, and 
who have not been in a position to acquire a practical 
familiarity with the subject, this presents many diffi- 
culties, and it is some of the most important of these 
which it is the object of this book to explain and clear 
away. 

The book therefore is intended simply as an in- 
troduction to the subject of electrical measurements, 
and no attempt has been made to enter upon any re- 
finements. 

The author believes, however, that it contains all 
that is essential for ordinary work, and trusts that 
those for whom the book was written, viz. the amateurs, 
will find in it all the aid they require in taking up this 
branch of the study of electricity. 

EDWARD TREVERT. 

Lynn, Mass., April 3d, 1894. 



GOKTEKTS. 



CHAPTER I. 

PAGE 

Electrical Units 7 



CHAPTER II. 
The Measurement of Resistance 14 

CHAPTER III. 
Current Measurements 71 

CHAPTER IV. 
Potential Measurement 99 



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ELECTRICAL MEASUREMENTS FOR 
AMATEURS. 



CHAPTER I. 

ELECTRICAL UNITS. 

Before entering upon the subject of measure- 
ments and measuring instruments, we will take a 
hasty survey of the units used and the manner of 
their derivation. 

When the matter of electrical measurements 
was first introduced, which was about the year 
1830 A. D., there was naturally a great deal of 
vagueness and uncertainty as to the proper 
method of expressing the results. Resistance 
was expressed in a number of ways and a 
number of standards were suggested, being 
usually expressed as the resistance of a wire of 
solid pure metal under specified conditions. 
These standards in time came to be looked upon 
as untrustworthy, as it was found that wires of 



8 ELECTKICAL MEASUREMENTS FOK AMATEURS. 

pure metal which were apparently similar in 
every respect, would often vary considerably in 
resistance, and that the resistance of any given 
wire depended largely upon its previous history. 
Matters were in this stage when Dr. Siemens 
proposed as the unit of resistance, the resist- 
ance of a column of pure mercury one metre 
long, one square millimetre in cross section, and 
at a temperature of 0^ centigrade. 

This had the advantange of being readily 
reproduced at any place on account of the 
uniformity of the molecular condition of pure 
mercury and the ease and accuracy with which 
the measurements of length and weight can be 
made. It is in this form that the present unit 
is defined, that is, as so many centrimetres of 
pure mercury with a cross section of one square 
millimetre. 

In 1 85 1 Webber proposed a system of electrical 
units, based upon the absolute system of Gauss, 
and this suggestion was subsequently taken up 
by the British Association for the Advancement 
of Science. The subject was investigated by the 
aid of an apparatus devised by Thomson, con- 



ELECTRICAL. UNITS. 9 

sisting of a coil of wire which was caused to rotate 
in the earth's magnetic field and a magnetic needle 
suspended at its centre. The induced current 
in the coil distorted the magnetic field and so 
deflected the needle. The great value of the 
apparatus lies in the fact that it is independent 
of the strength of the earth's field although it 
is affected by changes in its direction. 

After an extended series of experiments, what 
is called the British Association Unit or B. A. U. 
was produced. Its accuracy according to its C. 
G.N S. definition, was questioned later on and a 
re-determination of the value of the ohm shows 
that the B. A. U. is about 1.3 per cent too small. 
At a meeting of the Electrical Congress in Paris 
in 1884, it was decided to adopt for the time 
being, the value of the ohm as the resistance 
offered by a column of pure mercury, 106 cen- 
trimetres long, one square millimetre in cross 
section, and at a temperature of 0^ centigrade. 
The most careful recent experiments show that 
the true value of the ohm is very nearly given 
by a column of mercury 106.3 c- ^- 'oi^gj under 
the above conditions. 



10 ELECTKICAL MEASUREMENTS FOR AMATEURS. 

The unit recommended by the Paris Congress 
is called the legal ohm, and has caused much con- 
fusion at present on account of the existence of 
the two standards, results being sometimes 
expressed in B. A. units and sometimes in legal 
ohms. The unit used should always be desig- 
nated. It should be remembered in making reduc- 
tions, that the B. A. U. is .9867 of the legal ohm. 

The absolute system above referred to, -grew 
out of the necessity of having the results of 
physical researches in some form in which they 
could be easily compared among themselves. 

In it three fundamental units are chosen and 
from them are derived the others. The centi- 
metre, gramme and second are the units most 
commonly used in physical work, but a number 
of other units have been suggested, depending 
on the physical properties of various bodies, on 
which other ^'absolute" systems might be founded. 
The centimetre is the hundredth part of the 
length of a certain platinum bar, kept in the 
National Archives of France and measured 
under certain specified conditions. The length 
of this bar, called the metre, was supposed 



ELECTRICAL UNITS. 11 

when it was constructed, to be the ten millionth 
part of the quadrant of a meridian circle of 
the earth measured from the equator to the 
pole. Later determinations have shown that 
this is incorrect, so that now the meter is never 
defined as a portion of the earth's quadrant but 
as the length of a certain platinum bar as above. 

The gramme likewise is the one thousandth 
part of the mass of a piece of platinum also in 
the National Archives of France, which piece of 
platinum was made as nearly as possible, equal 
to sthe mass of a cubic decimetre of pure water 
at 4^ centigrade, its point of greatest density. 
What variation there is between the platinum 
standard and the cubic decemitre of water is at 
present uncertain, but the error is so small that 
the definition of the gramme as the mass of a 
cubic centimetre of pure water at 4^C. is close 
enough for all practical purposes. The mean 
solar second is the unit of time, and is defined 
as the gg^QQ part of the mean solar day. 

From these units are derived all others used 
in dynamics. Thus the unit of force, the dyne 
is the force of which acting for one second on a 



12 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

gramme of matter will impart to it a velocity of 
one centimetre a second. The unit of work or 
erg is the work necessary to overcome the force 
of one dyne through the space of one centi- 
metre. As this is extremely small the practical 
unit is taken as 10,000,000 ergs, and is called the 
Joule. The practical unit of the rate of working 
is the Watt, and is equivalent to one Joule per 
second. The units used in electrical measure- 
ments are all derived from these same fundamental 
units in a manner which need not be entered upon 
here. 

The C. G. S. units are usually far out of the 
range of practical observations, and in order to 
avoid the use of large numbers the practical units 
chosen are multiples of the C. G. S. units. Thus 
the ohm is 1,000,000,000 C. G. S. units, the volt 
100,000,000 C. G. S. units, the ampere is -^-^ of 
a C. G. S. unit, the Coulomb also -^-^ the C. G. S. 
unit, and so on through the list. 

Only three of these units enter to any great 
extent into most practical measurements, the volt 
or unit of electromotive force, the ampere or unit 
of current and the ohm or unit of resistance, and 



ELECTPvICAL UNITS. 13 

only measurements of these three quantities and 
of the activity, or rate of doing work in a given 
system, will be considered here. 



14 ELECTRICAL MEASUREMENTS FOR AMATEURS. 



CHAPTER II. 

THE MEASUREMENT OF RESISTANCE. 

Resistance measurements are made in a num- 
ber of different ways, by taking the volts and 
amperes of a current passing over the resistance 
to be measured, by a Wheatstone's bridge, by 
comparing the drop in potential around two 
resistances over which the same current is pass- 
ing, the value of one resistance being known, and 
by a number of special instruments which are 
modifications of one or more of the above methods. 

The first method of course depends upon the 

relation 

Ohm = Volts -^ Amperes 

E 
orR = ^ 

It is often of advantage to be able to get a 
resistance this way in cases where the resistance 
is different when the current is on from what it is 
when the current is off. The resistance of a bank 
of incandescent lamps where the hot resistance is 



THE MEASUREMENT OF RESISTANCE. 



15 



about half that of the cold is a case of this kind. 

The usual method of measuring resistances 
where they are neither very low nor very high is 
by means of the Wheatstone's bridge. This is a 
zero method and depends upon the ability to so 
adjust the ^resistances of a system of conductors, 




Fig. I. 

that the current through one of them is null. A 
galvanometer is placed in series with this conduc- 
tor and when it shows no deflection, the resistance 
measured can be calculated by simple proportion 
from the known values of the others. 

Suppose in Fig. i that a current from the 
battery is flowing around through the conductors. 



16 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



It will divide at A, one part going over the con- 
ductor A B D and the other over the conductor 
A C D, They will unite again at D^ and from 
thence return to the battery. The fall in poten- 
tial over the two branches must be the same, 




Fig. 2. 



since the potential at A is the same for both as is 
also the potential at D, The fall of potential over 



THE MEASUREMENT OF RESISTANCE. 17 

any particular portion of either branch will bear 
the same proportion to the fall of potential over 
the whole branch that the resistance of this portion 
bears to the resistance of the whole branch — from 
Ohm's law. Therefore, if the resistance of a por- 
tion, A B^ of one branch bears the same ratio 
to the resistance of the branch as the resistance 
oi A C does to the resistance of its branch, the 
fall of potential over A B and A C will be the 
same, although their resistances may be very 
different. As no current passes over a conduc- 
tor where there is no difference of potential and 
as the potential of the points B and C is the same, 
it is easily seen that no current passes over the 
conductor B C, which includes the galvanometer 
and that, therefore, there is no deflection of the 
galvanometer when a current is supplied by the 
battery. This, then, is the principle of the 
Wheatstone's bridge. The resistances of any 
three sides, a^ b and c, of the quadrilateral, whose 
resistances are known, are adjusted until a balance 
is obtained, when the resistance of the unknown 
side ;r, which was to be measured, is found from 
the proportions. 



18 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



a : b : : c : X, 

or a : c : : b : X. 

A form of Wheatstone's bridge, much used in 

making resistance measurements, is called the 

resistance box and is shown in Fig. 2 and is 



/»//»//) 




Fig. 3. 

represented diagramatically in Fig. 3. On the 
top of the box is a series of brass blocks spaced at 
small distances apart and with slightly taper holes 
between them, in which a brass plug can be 
inserted, and make a metalic connection between 



THE MEASUREMENT OF RESISTANCE. 19 

the two. Between each two adjacent blocks is 
connected a coil of wire of known resistance, 
which, when the plug is in its socket between the 
blocks, is short-circuited, but which is thrown into 
the circuit again by removing the plug. (See Fig. 
4.) The ^blocks are under-cut at each end so that 
the dust between them on the top of the box may 
be easily cleared off, and also so as to make the 




insulation resistance between the two blocks as 
great as possible. (See Fig. 5.) 

The lettering on the diagram of the box corre- 
sponds to that on the skeleton diagram, preceding, 
of the bridge. The arms, A B and A C, are called 
the proportional arms, and contain coils with 
resistances in them as indicated. The plugs 
pulled out of them will indicate the ratio of 
the resistance being measured to that unplugged 



20 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



in the rheostat arm, or arm of adjustable resist- 
ance. It is usually best to make this ratio, unity, 
by unplugging the same amount in each of the 
proportional arms and the resistance in each 
proportional arm should be as near as is possible 
to that you are going to measure. For instance, 
if you are measuring something in the neighbor- 
hood of 80 or 90 ohms, unplug the 100 coils in the 
proportional arms. In such cases as this the 
unknown resistance will be equal to the resist- 



)'« i 



Fig. 5. 



ance in the rheostat arm when balance is ob- 
tained, and can be read off directly. 

In some cases it is convenient to make the 
proportion greater or less than unity. For 
instance, a lOO-coil may be unplugged from one 
side and a lo-coil from the other, in which case, 
the reading on the rheostat will have to be multi- 
plied or divided by 10, according to the way the 
ratio arms are arranged. The rheostat arm is 
connected with one of the proportional arms by a 



THE MEASUREMENT OF RESISTANCE. 21 

heavy brass or copper connection. The resistance 
coils in this arm are arranged in series from i 
ohm to 4 ohms, from lo ohms to 40 ohms, from 
100 ohms to 400 ohms, etc. Any resistance 
within the limit of the set, in the case shown 
in the figure from i ohm to 11,110 ohms, can be 
obtained by a proper combination of the differ- 
ent coils. 

The most economical arrangement of the coils 
or the method by which the fewest number of 
coils can be made to cover a certain range of 
resistances is in a geometrical progression with a 
common ratio of two. It is rather more unhandy 
than the former arrangement to figure out just 
what resistance you may have unplugged or how 
to unplug for a given resistance, and the author 
thinks that the difference in cost is more than 
compensated by the inconvenience. 

The dial form of bridge is a vast improvement 
over either of the other forms in point of conven- 
ience. There is one dial for each digit, generally 
for thousands, hundreds, tens and units and some- 
times for tenths. The dial is composed of a 
central block of brass surrounded by ten other 



22 ELECTKICAL MEASUREMENTS FOR AMATEURS. 

blocks numbered from zero to nine, there being a 
plug hole between each outside block and the 
middle one. Between the adjoining outside 
blocks are resistance coils of i ohm each on 
the unit dial, of lO ohms each on the tens dial, 
etc. The central block of the unit dial is con- 
nected to the zero outside block of the tens and 
the central block of the tens to the zero outside 
block of the hundreds, and so on. Inserting the 
plug in any of the plug holes will throw into the 
circuit all the coils between that block and zero 
of that dial and, as the blocks are all numbered, 
it is easy to read off at once what the resistance is 
by taking the figures on the blocks where the 
plugs are. The proportional arms are the same 
as for the ordinary bridge. 

What is known as the slide wire or metre bridge 
is another form of the Wheatstone arrangement. 
The lettering in Figure 6 corresponds to that 
of the skeleton diagram given previously. The 
connections between the different parts of the 
apparatus are made by heavy copper strips, to 
reduce the resistance as much as possible. 
Between the copper strips, A and D, is stretched 



THE MEASUREMENT OF RESISTANCE. 



23 



a wire, generally of platinoid, which is soldered 
firmly to the strips. This wire is stretched above 
a graduated scale. A convenient length for the 
wire is about a yard or a metre, and it is usually 
made this latter length from the points of con- 
nection with the copper strips, and a metric scale 
placed beneath it. A rider of some convenient 



Batter 



:y 



yAAAAAli? 



vV^AA^A/| OC 



"'"'■■'■■l"''-'"--l li.l..l..l..l..l,.l..l..l..iJ I.,r,.l I..I..I I..I..I.....I, 




Fig. 6. 



form is made to sHde parallel to the wire and has 
a contact piece which, upon pressing a button or 



24 



ELECTEICAL MEASUREMENTS FOR AMATEURS. 




A 



2 



THE MEASUREMENT OF RESISTANCE. 25 

key, is made to touch the wire. In connection 
with the rider is some form of index for reading 
off its position on the metre scale. In many- 
cases a vernier is used. 

The gaps in the copper strips are provided with 
binding posts for the purpose of connecting in 
the known and unknown resistances. Let the 
unknown resistance be connected in at ;r, as 
shown in the diagram, and a known resistance at 
c. The battery is connected as shown. The 
galvanometer has one terminal connected at C 
and the other at B^ to the slider. The position of 
the slider is altered until the resistances on the 
two sides of the wire, on each side of the slider, 
are proportional to the resistances of the known 
and unknown coils. Then, assuming that the 
resistance of the slide wire is uniform, the resist- 
ance of the unknown coil can be obtained at once 
from that of the known coil and the scale reading. 
It is customary to number the scale from each end, 
so that the length of the wire on each side of the 
slider may be read off more easily. Within certain 
limits, lengthening the slide wire will increase 
the delicacy with which the measurements can be 



26 ELECTRICAL MEASUREMEJS^TS FOR AMATEURS. 

made. As an increase in the actual length of the 
wire itself would make a very awkward instru- 
ment, it is customary in most commercial instru- 
ments to leave the additional gaps in the copper 
connection strips into which may be inserted 
resistance coils which have the effect of adding to 
the slide wire resistance, just as though it had 
been lengthened. These resistances are selected 
so as to be nearly proportional to the known and 
unknown resistances. The point B^ at which the 
galvanometer connection must be made, will then 
lie on the slide wire. (See Fig. 7.) 

Slide wire bridges are made in special forms 
for special purposes. Where portability is an 
object, the wire is sometimes wound spirally 
about a cylinder. A stem projecting from the 
cylinder has threads of the same pitch as that 
of the wire on the cylinder and carries a radial 
arm, on the end of which is the contact piece. 
The scale is, of course, placed on one end of the 
cylinder, and divides the circle decimally, and 
marks on the radial arm indicate the number of 
turns of wire. (See Fig. 8). It is made up with 
binding posts on the base to suit the convenience 



THE MEASUREMENT OF RESISTANCE. 



27 



of the user. As the pitch of the wires will often 
be too great to thread the stem with, it is usual to 
double-thread the latter. The material for the 
cylinder on which the wire is wound should be 




Fig. 8. 



something not liable to alter its form. Wood, 
unless hard and thoroughly seasoned, is apt to 
warp and shrink, and leave the wire hanging 
loosely on it. I once saw a bridge, the cylinder 
of which was made of marble, and an excellent 
one it was too, but a trifle too heavy for carrying 
conveniently. The marble can be turned in any 
lathe which can be used for iron. 



28 



ELECTKICAL MEASUREMENTS FOR AMATEURS. 



Another very convenient form is one devised by 
Cardew, called his lightning conductor bridge. It 
was described in our ^' Electricity and its Recent 
Applications," and only a brief explanation of its 




Fig. 9. 



working will be given here. Fig. 9 is a skeleton 
diagram of the connections, in which B is the bat- 
tery and G the galvanometer. One terminal of 
the galvanometer is connected to the slider, which 
works along the slide wire d; a and b are the 
proportional arms, e is the wire connecting the 



THE MEASUREMENT OF RESISTANCE. 29 

binding post to the slide wire and ;r, as usual, the 
the unknown resistance. Ihe slide wire, d, is 
stretched above a scale, divided decimally and 
numbered from right to left, as the diagram 
stands. The advantage of this bridge is that 
the resistances are read off directly after the 
bridge hats been calibrated, thus obviating the 
calculation necessary on the ordinary slide wire 
bridge. 

W^ will give, briefly, the method of determin- 
ing the lengths of the various arms of the bridge, 
leaving it to the ingenuity of the reader to arrange 
them most conveniently on the board. You will 
have to know three quantities in order to make 
your calculations, the range of readings you desire 
for X, the resistance of the wire d, which is 
governed by its length, size and material, and the 
resistance of e. We have, when the maximum 
resistance is at x and the slider at its extreme 
left hand position, 

b __ c 

a e + x 

and when the resistance is at ;r = (supposing 
you have chosen for your lowest limit) 



30 ELECTRICAL MEASUREMEN^TS FOR AMATEURS. 





b 
a 


c-d . 
d + e * 








c 

e + x 


_ c — d 1 

- :t--^ and 
d + e 




cd + 


ce = ce 


+ cx — 


de- 


dx, 


c 


— ^^^+f which 


gives 






b _ 
a 


_ d 
~ x-d 







thus determining the value of the ratio of the 
proportional arms. We see from this that the 
value of d must be less than ;r, or the bridge 
will not work. Of course, the best value for d 
is one-half of that of x, but this is impracticable in 
cases where the unknown resistance is too high. 
The value of c is found from the equation 
c = ^ (x + e) 

. a ^ / 

and can be measured off on the wire with another 
bridge. The remaining portion of the wire is 
then divided up in the portion -. To gain length, 
the wire c — d and a and d can be carried up and 
down the length of the board several times, or 
even made into coils, which can be placed in a 
false bottom in the base board. It is best to 
standardize the bridge by comparison with coils 
whose values have already been determined. 
By inserting them at x you can accurately mark 



THE MEASUREMENT OF RESISTANCE. 31 

the points corresponding to them on the scale and 
then divide up the intervals decimally. As a slide 
wire will rarely be found to be uniform in resist- 
ance over its whole length, the more of these 
points that can be located in this way the better. 

We will now consider the practice followed in 
making resistance measurements with the instru- 
ments above described and then refer to a few 
other methods adapted to special cases. 

In ^making resistance measurements we gener- 
ally have some freedom in the choice of the 
resistances of the different arms of the bridge 
and by altering them to vary the sensibility of the 
arrangement, that is, vary the amount of ''throw" 
of the galvanometer for a given difference in the 
resistance of the adjustable arm. It may therefore 
be of considerable importance in some cases to 
know what is the most sensitive arrangement of 
the resistances. Prof. Thomas Gray has worked 
this out with the results given below. 

In Figure lo as shown, let r^ and r^ be the 
resistances of the proportional arms, rg, that of the 
adjustable arm ; r^, that of the unknown resist- 
ance ; rg, that of the galvanometer, and r^, that 



32 



ELECTRICAL MEASUEEME]>rrS FOR AMATEURS. 



of the battery. Then, if the battery and galvanom- 
eter resistances are fixed, the other resistances 
are to be chosen so that 

and r, = sjr, r, ^^ 
^4 having been roughly determined previously. 




If the resistances of the battery and the galvanom- 
eter are capable of variation, then the different 
resistances should all be equal to r^. Of course, 
on the supposition that its E. M. F. remains 



THE MEASUKEMENT OF MESISTANCE. 33 

constant, the lower the resistance of the battery 
the greater will be the deflection of the galvanom- 
eter for any given adjustment of the bridge. In 
general, however, such a degree of refinement is 
unnecessary. 

The resistances of 7^-^ and ^2 may be chosen at 
almost arty convenient values and the galvanom- 
eter and battery then connected so that the 
greater of the two connects the junction of the 
two arms with the greatest resistances to that of 
the two arms with the least resistances. The con- 
nections should be arranged with keys in both 
battery and galvanometer circuit, which are closed 
by simply pressing down. Two separate keys can 
be used, but interfere somewhat with rapid work if 
they require both hands to work them. A key 
can be arranged so that depressing it a short 
distance closes the battery circuit and still further 
depressing closes the galvanometer circuit. In 
this way one hand is left free to manipulate the 
plugs or slider of the bridge. Figure 1 1 shows 
such a key. It is mounted on an ebonite block 
and pillars. The key itself is made of spring 
brass and has an ebonite button on the end. 



84 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



Silver contacts are placed between the first two 
arms and between the second and third are 
ebonite insulators, then silver contacts again 
between the last arm and the block. It is 
better to mount the arms for the battery and 
that for the galvanometer on separate pillars so 
as to decrease the liability to leakage between 
them. 



Ca.i. 



anofneCer 



Contacts 




Fig. II. 

The insulating pieces should be kept carefully 
cleaned. Suitable binding posts may, of course, 
be provided for the galvanometer and battery 
connections. The battery should consist of two 
or three cells. Gravity and Leclanche are both 
good for this purpose, the latter especially so for 



THE MEASUREMENT OF KESISTANCE. 35 

general work, where the current is only needed 
for short periods at long intervals. 

There are now a number of good dry batteries 
on the market which are excellent for portable 
testing sets. The styles of galvanometers used 
for resistance measurement are as various as the 
makers. , They usually consist of a coil of wire 
within which is suspended a magnetized needle. 
The needle is usually cemented to a thin, plane 
mirror, about | of an inch in diameter, which is 
used either to reflect a spot of light upon a 
darkened scale, or in connection with a telescope 
in reading an illuminated scale. It is customary 
to have a directing magnet fixed to the galvanom- 
eter for regulating the strength and direction of 
the field in which the needle works. It usually 
consists of a bar of magnetized steel mounted 
in a horizontal position upon a vertical rod 
on which it can slide up and down or rotate. 
(See Figure 12.) By raising or lowering this 
magnet we change the strength of the field. 
Thus, if, as in some cases it is desirable, we want a 
very weak field, so that the needle will be deflected 
by a feeble current in the galvanometer coil, we 



86 ELECTRICAL MEASUREMENTS FOR AMATEURS. 




Fig. 12. 



THE MEASUREMENTS OF RESISTANCE. 



37 



turn the north seeking pole of the directing 
magnet to the north and then bring it nearer 
to the needle until the earth's magnetic force is 
almost neutralized. If on the contrary we want 
a very strong field, either to reduce the disturb- 
ing effect of some outside force, or to make the 
needle take up its position more quickly, we turn 
the north seeking pole of the directing magnet 





south and bring it down to the needle until the 
desired effect is obtained. 

Galvanometers are sometimes made with two 
separate needles or sets of needles, one inside 
and one outside the coil or, as sometimes con- 
structed, in another coil. (See Figure 13.) 



38 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

The two systems of needles are rigidly con- 
nected and have their north poles turned in 
opposite directions. The result of this would 
be, if the needles were exactly similar in dimen- 
sions and magnetic strength, that they would tend 
to take up no particular position in a uniform 
magnetic field. Practically, they never are the 
same. One is always slightly stronger than the 
other and determines the position assumed. The 
directing magnet also acts more strongly on the 
needle nearest it. The effect of reversing the 
needles, however, does not weaken the effect of 
the coils upon them, but increases it. The one 
outside of the single coil will, of course, tend to 
turn in the opposite direction to that of the 
needle inside, if both are headed in the same 
direction, and therefore reversing their poles 
makes them both turn in the same direction. 
Where two coils are used, the current in the 
lower one goes in the opposite direction to that 
in the upper coil. 

Some galvanometers are arranged with coils 
of different resistances which can be interchanged 
at will. A very useful form of galvanometer is 



THE MEASUREMENT OF BESISTANCE. 



39 



that of d' Arsonval. In it the coil is made 
movable and what corresponds to the needle, 
stationary. The coil is wound in a rectangular 
form and is suspended between two wires by 




Fig. 14. 



which the current is carried to and from it. (See 
Figure 14.) The mirror is attached to the coil. 
The field is supplied by strong, permanent horse- 
shoe magnets and is strengthened by a soft iron 
core in the inside of the coil, to which, however, 



40 



ELECTKICAL MEASUREMENTS FOK AMATEURS. 



it is not attached. This form of galvanometer 
has. several excellent features. It can be made 
very sensitive and it is not influenced by outside 
magnetic disturbances. On account of the 
strong artificial field, it comes to rest almost 
at once and it makes a good portable instrument. 
The galvanometer deflections are usually read from 
a spot of light reflected on a darkened scale or by 




Fig. 15. 

means of a telescope in conjunction with a scale. 
Where the first method is used we have a scale 
mounted, something as shown in Figure 15. The 
scale is about two feet long and is graduated in 
millimetres. Zero is placed in the middle and the 
graduations are numbered to the right and left of 
this. The board to which the scale is glued is 
about ten inches high and supports a shade which 



THE MEASUREMENT OF RESISTANCE. 41 

is sometimes made so as to turn up or down. 
Below the scale is a hole about | of an inch in 
diameter, across which is stretched vertically a 
fine wire. A paraffine lamp is set up behind the 
scale with its flame opposite the hole and its light 
passing through the hole falls on the galvanom- 
eter mirror and is reflected back to the scale. By 
means ofv a suitable lens between the lamp and 
galvanometer, the image of the wire across the 
hole is focused on the scale. The deflection 
of the galvanometer is thus readily indicated on 
the scale and is moreover multiplied by two, since 
according to the well-known law of optics the 
angle between the incident and reflected ray of 
light is double that between either ray and a 
normal to the mirror, and the galvanometer deflec- 
tion is the angle between the incident ray and the 
normal to the mirror. When telescopic readings 
are taken we have an ordinary reading telescope 
with cross hairs in it and generally some means 
of clamping a metre scale to its base. The scale 
must, of course, be at right angles to the axis of 
the telescope and with its zero in a vertical 
line with this axis. The galvanometer is set up at 



42 ELECTRICAL MEASUBEMENTS FOK AMATEUKS. 

about a metre's distance from the scale, and when 
it is properly levelled and adjusted, its mirror is 
in such a position that when looking through the 
telescope the scale can be seen reflected in it. 
(See Figure i6.) 

The scales for reading telescopes are made with 
the zero in the middle and the figures are printed 



Fig. 1 6. 

backwards so as to come right in the telescope, as 
it is customary to make them without an erecting 
lens. It will be found necessary in most cases to 
illuminate the scale with a row of small gas jets in 
front of it. When no current is passing through 
the galvanometer the telescope is so adjusted that 
the zero of the scale coincides with the vertical 



THE MEASUREMENT OF RESISTANCE. 43 

cross hair. A galvanometer deflection is shown in 
the telescope, by the scale apparently moving past 
the cross hairs. More accurate readings may be 
taken in this manner than by the other, but such 
refinements are usually out of place in resistance 
measurements and as this method is so much more 
cumbersome and unhandy than the other, it is gen- 
erally discarded. 

The location of the instrument should be care- 
fully chosen. It should be as free as possible from 
vibration. The galvanometer, especially, should be 
set upon a firm foundation, a pier, if possible, which 
has no connection with the floor of the room. It 
is not necessary that the scale and lamp should be 
so carefully placed, but even with them it will be 
found of advantage to place them in as quiet a spot 
as possible. Every cause of magnetic disturbance 
should be removed. While it is best to be away 
as far as possible from all masses of iron, station- 
ary masses are not objectionable, providing they 
do not change in their magnetic strength, for 
instance, as do the fields of a dynamo. Wires 
carrymg heavy currents should be avoided. Mag- 
netic shields around the galvanometer are some- 



44 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

times suggested, but are not much good practically, 
as they are too apt to become variably magnetized 
themselves. The galvanometer scale should be 
set up in a darkened corner so that the light spot 
may be clearly seen upon it. 

In setting up the galvanometer our first care 
is to get it levelled and the plane of its coils in the 
magnetic meridian. This last is best accom- 
plished with a prismatic compass, by the aid of 
which we make a north and south chalk mark on 
the slab on which the galvanometer rests. Then 
by the aid of a long, straight stick clamped to the 
face of the coils, we set the coils parallel to this 
chalk mark. The position of the galvanometer 
levelling screws should now be marked on the slab 
and the galvanometer removed. Make a small 
hole or depression just large enough to receive 
the end of one of the screws where one of the 
marks is, a slot just wide enough for the point of 
another screw and leave the third plane. By the 
aid of the hole and slot you can always put your 
galvanometer back again in exactly the same place 
whenever it has been necessary to remove it. 
Two holes would be sufficient were it not for the 



THE MEASUREMENT OF RESISTANCE. 45 

expansion of the metal from changes of tempera- 
ture. Now put the galvanometer in place and 
level it and on a line perpendicular to the coil and 
one metre away place the scale which must also 
be perpendicularly intersected by this line at its 
centre or zero mark. Set up your lamp behind it 
and fasten a piece of mirror to the middle of the 
front of the^ coil by an elastic band, and see if the 
image reflected on the scale is on the zero mark. 
If not, the scale must be moved until it is. Take 
off this piece of mirror and also the controlling 
magnet and raise the needle until it swings freely 
at the centre of the coil. If the supporting fibre 
has not been twisted the image reflected from its 
mirror should coincide with the zero mark of the 
scale. If it does not, the fibre should be twisted 
so as to bring it there. In making this adjustment 
be careful that all movable iron or steel is removed, 
even articles of that kind in your pockets. I have 
known men who claimed that their instruments 
were so sensitive in this state that the iron in a 
man's blood was sufficient to deflect them. I 
have learned, however, that the statements of all 
electricians are not to be trusted implicitly. The 



46 



ELECTEICAL MEASUREMENTS FOR AMATEURS. 



controlling magnet may now be replaced and the 
galvanometer is ready for work. We must first, 
however, speak of the galvanometer-shunt. Figure 
17 shows a plan of a familiar form. 




Fig. 17. 



The galvanometer terminals are connected to 
the binding posts on a and e, from which are also 
the lead wires to the circuit in which the galva- 
nometer is placed, e and /are connected together 
by a wire of low resistance, and between a and b'> 
a and c and a and d are coils whose resistances 
are respectively \, -^ and -g^-g that of the galva- 
nometer. Leaving all the plug holes open puts 
the galvanometer directly in the circuit. Plugging 



THE MEASUKEMENT OF RESISTANCE. 47 

a and e^ short circuits it. Plugging /and b shunts 
the galvanometer with \ of its own resistance and 
so cuts down its current to -^ of what it was 
formerly. Likewise plugging between f and c 
and / and d cuts down the galvanometer current 
to y^ and y oVo" ^^ ^^^ value when the shunt is open. 
The shunts are, of course, to reduce the sensibility 
of the instrubnent and are used when making the 
first adjustments of the bridge when the resist- 
ance to be measured is not known very closely 
beforehand, so as to keep the galvanometer needle 
from swinging excessively or banging itself to 
pieces if there are stops. We are now ready 
to connect up our bridge. The galvanometer 
and scale are supposed to be on or a little below 
the level of the eye, and the resistance box or 
bridge may be set on a table of convenient height 
between them. Make the connections as indi- 
cated in the previous bridge diagram. 

We will suppose first that your bridge is a box 
of resistance coils. Put a small resistance between 
the '^unknown,'* binding posts and unplug — say 
10 from each of the proportional arms and 
leave the rheostat or adjustable arm entirely 



48 ELECTRICAL MEASUREMENTS FOE AMATEURS. 

plugged in. Plug in the -^^-^ galvanometer- 
shunt and then depress the key, closing the 
battery first and galvanometer second. This is 
a very important step, as the self-induction in 
the resistance to be measured is often very great, 
especially if it is a heavy magnet and this self- 
induction will cause the galvanometer light spot to 
fly all over the scale if its connection is made too 
soon after the battery circuit is closed. Then on 
pressing the galvanometer key the light spot 
should move off to one side of the scale or some- 
thing is wrong with the connections. Next, with 
everything else the same as before, unplug infinity 
in the rheostat arm and on pressing battery and 
galvanometer keys the light spot should move off 
in the other direction. These directions should 
be noted and remembered, so that in the future 
you may be able to tell at once whether you have 
too little or too much resistance unplugged in the 
rheostat arm. Replacing the infinity plug, unplug 
what you think is about the resistance of the 
unknown and try that. The direction in which 
the light spot moves will tell you whether it is too 
much or too little. Keep on with your adjust- 



THE MEASUKEMENT OF RESISTANCE. 49 

ment until you have it about right and then 
remove the galvanometer-shunt and make the final 
adjustments, that is, get a resistance into the 
rheostat arm, such that the light spot does not 
move from zero, whether the keys are raised or 
depressed. The resistance unplugged will bear 
the same ratio to the unknown that the propor- 
tional arms do to each other. It will often happen 
that unplugging the smallest unit you have in the 
rheostat arm will cause the spot of light to go to 
one side of the zero and plugging it in will cause 
the spot to go to the other side of zero, thus indi- 
cating that the true value of the unknown resist- 
ance lies between these limits. If it is desired to 
go below this smallest unit it is generally sufficient 
to take the deflections on each side of zero as pro- 
portional to the difference of the true value from 
that indicated by the rheostat. Thus, if the galva- 
nometer spot should be at -f- 15 when 98 ohms 
were unplugged and — 10 with 97 ohms, we know 
that the true value of the unknown resistance lies 
somewhere between 97 and 98, and that it is fair 
to assume it to be about 97.4 ohms. 

It is not safe to divide differences of more than 



50 ELECTBICAL MEASUREMENTS FOR AMATEURS. 

one or two per cent by this method of deflections, 
as the galvanometers used for resistance measure- 
ments do not follow the tangent law except for a 
few degrees on each side of zero. If measure- 
ments are made of smaller quantities it is better 
to change the proportional arms to suit. Measure- 
ments of small resistances should, however, never 
be made on a box of resistance coils if accuracy is 
desired. There are too many chances of error in 
bad contacts, especially in the plug holes, and of 
contacts of variable resistance in the leads. 

The lead wires should be measured after each 
resistance measurement and this measurement 
deducted from the value already obtained. This 
is done, of course, by simply disconnecting the 
object whose resistance was being measured and 
clamping the free ends of the leads together. 

Whenever the resistance of an object in a 
different part of the room or building is to be 
measured and there is enough of this sort of work 
to make it worth while to put up permanent lead 
wires it is a good plan to introduce an additional 
resistance in them which will bring up the total to 
some even number of ohms. This makes the 



THE MEASUREMENT OF RESISTANCE. 



51 



calculations simpler for getting at the unknown 
resistance and thus lessens the liability of errors. 
Of course, if very accurate results are desired, 
the leads must be measured each time, on account 
of the error introduced by variations of tempera- 
ture. If the wires are made large, however, this 




error will be so small a percentage of the whole 
that it may in most cases be neglected. 

It is desirable in some cases to know the resist- 
ance of the galvanometer which is used with the 
bridge, and often there is no other galvanometer 
which can be used to measure it in the ordinary 
way. A second galvanometer may be dispensed 



52 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

with, if Thomson's method is employed. Figure 
1 8 shows the arrangement. The galvanometer is 
connected in the;ir or ''unknown" arm of the bridge 
the same as any other unknown resistance would 
be and in the place where the galvanometer usually 
would be is a key. It is easily seen that when 
perfect balance is obtained in the four resistance 
arms, opening or closing the key can have no 
effect on the current passing through these arms. 
The idea is, then, to pass a current through 
the bridge which will give a readable deflection on 
the galvanometer and then adjust the resistance 
arms until opening or closing the key makes no 
change in the galvanometer deflection. It will 
be necessary to cut down the battery current, by 
shunting it otherwise the current will be much too 
great to work with. A resistance should be 
included between the battery and the shunt in 
order to keep the battery current constant. Now 
press the battery key and putting the directing 
magnet low so as to strengthen the earth's field, 
turn it about until the deflected light spot is 
brought back on the scale. Then press the key 
ivhich is in the former galvanometer circuit and 



THE MEASUREMENT OF RESISTANCE. 



53 



adjust your rheostat arm until opening or closing 
this key has no effect on the galvanometer. It is 
suggested that in the case of differential galvanom- 
eters, it is a good plan to measure only one coil 
at a time and to send a current from another 
battery through the other coil, which will nearly 
balance the current in the coil being measured. 



Standard 

■n 



60] 10 lo o| 6 lo 



unKnown 



m 



Fig. 19. 

This increases the delicacy with which the 
measurements may be made, as it is then un- 
necessary to lower the directing magnet. 

The principle of the SHde Wire Bridge has 
been explained above, and it only remains to give 
a brief account of the method of working it. 

When only rough measurements are desired, the 
resistances of the connecting copper strips may 



54 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

be disregarded and the connections made as shown 
in Figure 19. A standard or known resistance 
will be required to compare the unknown resist- 
ance with. The operations are similar to those 
with the box of coils except that in this case the 
proportional arms are altered instead of the arm 
in opposition to the unknown. The battery key- 
should always be pressed first, as in the other case. 
The slider contact serves for the galvanometer 
key in this case. When balance is obtained, the 
lengths of the slide wire on both sides of the con- 
tact are used to form a ratio which is equal to that 
of the known and unknown resistances. When our 
measurements are to be made more exact a num- 
ber of corrections and allowances must be made. 
The thermo current from, the junction of the 
platinum contact with the bridge wire, notwith- 
standing the fact that it is so small, will noticeably 
affect a galvanometer which is at all sensitive 
when it is connected as shown in Figure 19. By 
interchanging the battery and galvanometer con- 
nections, we do away with the evil at this point, 
and while it may exist now at the soldered connec- 
tions of the wire to the copper strips, it is to a much 



THE MEASUEEMENT OF RESISTANCE. 



55 



smaller extent and may be made insignificant if 
we use care in keeping the two ends of the bridge 
at a uniform temperature. Wrapping them around 
with some non-conducting material will do this. 
By pressing the contact key when the galvanom- 
eter is connected, as at first it can be seen if the 
error will be sufficiently great to make the change 




Fig. 20. 

advisable as indicated above. It may happen that 
the contact piece does not touch the wire at the 
point indicated on the scale. This may be cor- 
rected by making two measurements, the second 
with the known and unknown resistances inter- 
changed. The resistances of the end pieces, 
although small, cannot be entirely neglected. 
In Figure 20 let r-^ = the resistance of the 



56 ELECTRICAL MEASUREMEI^TS FOR AMATEURS. 

copper strip to the right and r^ = the resistance 
of the left hand strip. Let A and B be the resist- 
ances which we are comparing. Also suppose the 
scale to be in error by a quantity d^ that is to say 
that the reading from the slider does not corre- 
spond with the point of contact on the wire. 
All resistances are expressed in terms of divisions 
of the slide wire, which we will suppose is divided 
into looo equal parts. 

Now, on balancing up in the usual way, let x^ 
be the reading obtained. The true reading will 
then be x^ -\- <^and the ratio of the resistances A 
and B will be 

A_ r, +xi+d 
B 1*2 + lOOO — (x-,^ -|- d) 
Interchange A and B and a new reading will be 
obtained, say;r2. The new ratio will then be 

A _ r^ + lOOO — (X2 + d) 
B n + X2 + d 

Adding the numerators and denominators of the 
fractions together, we get a ratio, 

A_ I OOP + r^ -f 1^2 + (xi— X2) 
B 1000 r^ + rg — (xi — X2) 

which is free from d and in which r^ and x^ which 



THE MEASUREMENT OF RESISTANCE. 57 

are small quantities are added to large ones, and 
since they are small and their values not definitely- 
known, we may, without great error, omit them 
from the equation and use the formula proposed 
by Siemens. 

A looo -f- (xi — ^2) 

B 1000 (X;^ — X2) 

This formula will be most nearly exact when 
the quantities x^l ^^^ ^2 ^^^ nearest equal. To 
determine the values of r^ and r2 let the coils A 
and B be two whose values are known and whose 
ratio is about 100 to i. Supposing there is no 
scale error 

A_ r, + xi 

B 1";^ + 1000 X^ 

and after interchanging A and B 

A i"2 + 1000 — X2 



B r-L + X2 
Solving these equations for r^ and r2 we get 

B x-iL — A ^2 



and 



1— A — B 



B (1000 — ^ X2) — A (1000 — x-^) 

"2 x^ B 



58 



ELECTBICAL MEASUREMENTS FOR AMATEURS. 



The sensitiveness of the bridge may be greatly 
increased as stated above, by lengthening the slide 
wire, or (what amounts to the same thing) by 
adding resistances in series with it. (See Fig. 21.) 

— ^Illlllh^n 



n. ^ An 

0/WVVA/V\ /WVVV\ /VWWv 

_ "0"^ \6 6 01 16 061 (c 










Fig. 21. 

These resistances are shown above as R^ and 

Rg. The ratio A to B when these resistances are 

in, is 

A ^ r , + Ri xi 

B ^2 + ^2 + 1000 X;^ 

Interchanging A and B the equation becomes 

A ^ r^ + R2 + 1000 — X2 
B ri + Ri + X2 

Adding numerators and denominators together we 

obtain 

A_ ri 4- r^ + R^ + R2 + looo + (^i — ^2) 

B r, + r2 + Ri + R2 + 1000 — (xi — x,) 



THE MEASUREMENT OF RESISTANCE. 59 

With any given values of R^ and i?2> ^he range 
over which readings may be taken is reduced from 
what it would be if they were omitted entirely, 
but at the same time the sensitiveness o£ the 
bridge is increased. Of course, it only necessary 
to make a proper chbice of R^ and R2 to obtain 
any readings we desire. The values of R^ and 
R2 must be determined in terms of bridge-wire 
divisions before they can be inserted in the 
formula. To do this remove R2 from the bridge 
and close the opening by the copper connection. 
With A and B known the value oi R-^ will be 

Ri = g (1000 — xi + r V 2) — xi — ri 
So also with R-j^ bridged, the value of R2 will be 

1^2=^ (l"l + ^2) — 1*2 — 1000 + X2 

Mercury cups are used in making the connec- 
tions to the coils when careful work is to be done. 
These cups are simply holes bored in blocks of 
wood and filled with mercury. In the bottom of 
each cup is placed a disk of copper which has 
been amalgamated. In making connections it is 
only necessary to dip the ends of the wires (which 



60 



EL.ECTEICAL MEASUREMENTS FOR AMATEURS. 



have previously been amalgamated) into the cups, 
making sure that they touch the bottom. 

For making comparisons of resistance, a num- 
ber of coils should be on hand whose resistance 
and temperature coefficient is accurately known. 

The commercial form of standard ohm found in 




Fig. 22. 

most laboratories is shown in Figure 22. The 
standard coil is wound within the lower cylinder 
which, when being used is placed in water up to 
the shoulder* The ends of the coils are 
attached to the thick copper Avires coming up 
through the top and which are dipped into the 



THE MEASUREMENT OF RESISTANCE. 61 

mercury cups spoken of above, when the coil is 
being used. A therm meter is introduced through 
the hole in the top to take the temperature. 

There are often cases when it is desirable to 
get the resistance of some object while a current 
is passing through it, as, for instance, an incan- 
descent lamp whose resistance when ^'hot" is 
is about half of what it is when cold. About the 
only way this can be done is to take the volts and 
amperes of the current passing through the lamp 
and calculate the resistance from these. 

Professors Ayrton and Perry have designed an 
instrument called an ohmmeter for measuring the 
resistance of a circuit over which a current is 
passing. There are two coils in the instrument 
whose centres are coincident and whose planes 
are at right angles. A small needle is sus- 
pended at the centre of the coils so as to revolve 
about the line of intersection of the planes of the 
two coils as an axis. This needle moves an index 
over a scale above, graduated to read in ohms. 
One of the coils is of thick wire and is placed in 
series with the circuit whose resistance is to be 
measured, the other is of fine wire and is placed in 



62 ELECTKTCAL MEASUREMENTS FOE AMATEUES. 

parallel to the circuit. When a current is flowing 
through the instrument in the manner indicated, 
the resultant direction of the magnetic field in the 
centre of the coils will depend upon the relative 
intensities of the currents in the coarse and fine 
wires and as any variation of the strength of cur- 
rent in the main circuit will change the two 
currents in the instrument in the same proportion, 
it follows that each deflection of the needle will 
correspond to a particular resistance, since this 
resistance is the only thing that changes the rela- 
tive value of the currents. 

We will now take up briefly some special cases 
of resistance measurements. 

Neither very high or very low resistances 
can be measured by ordinary methods with any 
approach to accuracy. The resistances of the 
contacts in making low resistance measurements 
is often greater than the resistance of the object 
itself. We have then in general, to adopt some 
method by which this contact resistance way does 
not enter into question. One of these methods 
is with a differential galvanometer. Figure 23 
shows the arrangement. 



THE MEASUREMENT OF RESISTANCE. 



63 



A B is the low resistance to be measured. C 
D is a standard bar graduated decimally and 
joined to A B by B C. A current is passed over 
the standard and unknown resistances in series. 
From two points on ^ ^ between which it is 
desired to take the resistance, two wires are led 
to one coil of a differential galvanometer and the 
other coil is connected to E and D on the standard 



-AA^^V| 



AAAAA- 



FiG. 23. 

bar. The contact E is arranged so as to slide 
along the bar. 

The differential galvanometer is one with two 
coils insulated from each other and acting upon a 
magnetic needle placed on their axis between 
them. If a current is passed through one coil and 
in such a direction as to oppose an equal cur- 



64 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

rent in the other coil there will be no effect upon 
the needle at the centre. 

Before using the galvanometer, its coils should 
be coupled in parallel in such a manner that the 
currents will oppose each other. There should be 
no deflection of the galvanometer-needle with the 
current on or off ; but if there is a deflection a 
sufficient resistance should be inserted in one of 
them to bring the needle back to zero. 

In making measurements by this method the 
sliding galvanometer connection on the standard 
rod should be moved backwards or forwards 
until there is no galvanometer deflection, when 
the unknown resistance will be equal to the 
resistance included between the galvanometer ter- 
minals on the standard bar, since the same 
current is passing over each, and the fall of poten- 
tial is shown by the galvanometer to be the same 
for both resistances. This method evidently gets 
around the difficulty with the contact resistances, 
since the only contact resistances we have to deal 
with are those of the galvanometer connections 
and they are so small in comparison with the resist- 



THE MEASUREMENT OF RESISTANCE. 65 

ance of the galvanometer itself that they may be 
safely neglected. 

The current used must not be strong enough to 
raise the temperature of the resistances noticeably, 
as this might introduce a very considerable error 
in the results. 

The standard resistance should be some- 
where near in value to the resistance to be 
measured and may be made with same apparatus. 

A one-ohm resistance will be required to start 
with, which is placed between the terminals E D 
in the diagram. The total resistance in the cir- 
cuit of the galvanometer coil connected to this 
side is then increased ten times. The points A 
B on a. thick wire of convenient length are then 
determined and the resistance between them will, 
of course, be one-tenth of an ohm. With this 
wire as the standard, the same process may be 
used to lay off one one-hundreth of an ohm on 
thicker wire. Then with the terminals on the 
standard fixed a short distance apart, find a length 
corresponding on the other wire which balances 
it and see if this length is the sam.e for every part 
of the wire. If it is, then the wire may be divided 



66 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

up evenly on a decimal scale. But if the resist- 
ance of the last wire is not the same for each 
equal division of its length, then a definite resist- 
ance must be taken on the auxiliary wire and the 
length for the corresponding resistance determined 
for each portion of the other wire. The lengths of 
the decimal divisions at the different parts of the 
wire will then be proportional to the lengths just 
determined. 

There are a number of other methods for mak- 
ing low resistance measurements, but the above is 
sufificiently general to cover most cases met with 
in practice. 

For very high resistances a special method is 
also necessary. The one we will describe requires 
a sensitive galvanometer and a large battery — say 
lOO or 200 cells, which should be well insulated. 

The galvanometer, battery and resistance to be 
measured are joined in series and the deflection 
of the galvanometer noted. The unknown resist- 
ance is then removed and in its place is inserted a 
high known resistance. 

In Fig. 23^ let E represent the battery E. M. F., 
B, its resistance; X, the unknown resistance; G, 



THE MEASUREMENT OF RESISTANCE. D» 

that of the galvanometer; S, that of the galvanome- 
ter-shunt; R^ the resistance inserted in series with 
the galvanometer; D, the galvanometer deflec- 



3 



R 



& 



Fig. 23>^. 



tion, and c a constant by which this deflection 
must be multiplied to give volts, we have the fol- 
lowing equations : 

EG ^ 

=: C D 

G + B + X 
for the first case, and 

^ S + G ESG 



B + R + 



-SnG~~(B-fR)(S + G) + SG 



cD 



S + G 
and from these two equations we find that 

X=.g-i(B + R + G+ ^^ + ^^ ^ ) - (B + G) 



68 



ELECTKICAL MEASUREMENTS FOE AMATEURS. 



where if X be great in comparison with the 
rest of the circuit, (B -|- G) may be dropped. 

Everything must be carefully insulated in mak- 
ing this test. The methods of making connections 
to the specimens will, of course, vary in every case. 
For insulators of the cup-shaped variety, such as 
are used in telegraph work, they may be filled with 




Fig. 24. 
mercury within half an inch of the top and placed 
in a vessel containing mercury up to within half 
an inch of their brim and the connections made in 
the mercury. The rims should be coated with 
paraffine. 

Cables may be coiled up in a zinc trough 
full of water. The two ends are brought out and 
dried. One is carefully insulated and the other 
connected to one of the galvanometer terminals. 



THE MEASUREMENT OF RESISTANCE. 69 

and the other terminal goes to the zinc trough. 
(See Fig. 24.) 

Leaks in lighting installations may be detected 
by an ordinary voltmeter if their resistance is not 
too great compared to that of the voltmeter. The 
voltmeter is first placed directly on the dynamo or 
battery and then in series with the leak and from 
these readings and the known resistance of the 
voltmeter, the leak resistance is calculated. Let- 
ting L = leak resistance, R =z voltmeter resist- 
ance, V = reading of voltmeter direct from dynamo 
or battery, and v = voltmeter reading when in 
series with leak. Then 

V_ L + R 



V R 

R V 



or 



— R 



We will close this chapter with a short descrip- 
tion of the method of measuring the resistance 
of a battery. 

Battery-resistance is rather an indefinite term, 
as it changes somewhat with the strength of the 
current and is also apt to increase after the current 
has been passing for a while. 



70 ELECTEICAL MEASUREMENTS FOR AMATEURS. 

What we generally want to know, however, is 
what is the resistance for a given external resist- 
ance. 

Suppose E to represent the battery E. M. F. 
on open circuit; R^ the external resistance, and 
B^ the battery resistance, and suppose Fto be the 
voltage at the poles of the battery when it is 
working on the given external resistance. Then 



R 


E 

+ 


B 


_ V 
~ R 


or 


B 





E- 


-V 


R 



V 

Therefore with a potential galvanometer or high 
resistance voltmeter, measure the battery E. M. F. 
on an open circuit, and again when it is working 
on the given resistance. The values obtained sub- 
stituted in the above formula will give^. 



CURRENT MEASUREMENTS. 71 



CHAPTER III. 

\ 

CURRENT IMEASUREMENTS. 

The practical measurement of current is usually 
made by means of some instrument which has 
been calibrated to read directly in amperes by 
means of a graduated scale and a pointer. 

Instruments of this sort in general do not work 
according to any well defined law by which their 
indications may be predicted accurately before- 
hand and must be compared with some standard. 

The two methods of checking up an instrument 
most commonly used are with an absolute tangent 
galvanometer and by a copper or silver voltmeter. 
The former method, although not so much used 
as the latter, will be outlined here. 

It is rather cumbersome, as an accurate knowl- 
edge of both the constants of the instrument and 
the strength of the magnetic field in which it 
works is required. This magnetic field will, in 
general, be the horizontal component of the earth's 
magnetism, commonly designated as H. It must 



72 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



be determined in the place in which the galvanom- 
eter is to be used, as a small variation in locality 
may materially change its value. This is especially 
true when there is any iron about. Iron itself is 
not very objectionable if it is stationary and does 
not change its magnetic strength. 

To measure the value of H, a magnetometer 
will be necessary. (See Figure 25.) It consists 



/^?^ 




Fig. 25. 

of an upright piece of wood about 6 inches high 
and ^'^ thick by i^^^ wide, mounted on a triangular 
base ^ of an inch thick and 5 inches on a side, 
which is provided with three levelling screws. An 
inch from the lower end of the upright an opening 
is cut about the diameter of a five-cent piece and 
twice as deep as the five-cent piece is thick. 

From this opening to the top of the upright a 
small groove is cut, and at the top of the groove 



CURRENT MEASUREMENTS. 73 

an adjusting brass pin is fitted. This pin takes 
a fibre of cocoon silk, by which is suspended at 
the circular opening below a small galvanometer 
mirror, with a bit of magnetized sewing needle 
cemented to its back. 

The deflections of this needle are to b6 observed 
by means of a spot of light on a scale placed at a 
metre's distance, as described in the chapter on 
Resistance Measurements, or with a telescope. 

To prevent the needle being disturbed by 
vagrant currents of air, a strip of glass is placed in 
the front of the upright piece and held by rubber 
bands. 

Of course, no iron must be used in constructing 
the magnetometer. 

A wooden scale graduated in centimetres is 
clamped to the base board in the rear, and on it 
slides a cork through which the magnet to be 
tested is thrust at right angles to the scale. 

The test magnets are made of knitting needles 
about 7 centimetres long. (The metric system is 
used in designating lengths which occur in calcu- 
lations, so as to avoid trouble in changing from 
one system to another.) 



74 



ELECTBICAL MEASUREMENTS FOR AMATEURS. 



They are first annealed by heating and then 
straightened and smoothed up on the ends. 

Half a dozen are then bound into a bundle with 
iron wire and again heated to a cherry red and 
plunged vertically into cold water. Select those 




Fig. 26. 



which appear to be straight and magnetize them in 
a helix. 

The magnets are to be suspended under a glass 
shade by means of a silk fibre and a paper stirrup. 
A bottle with the bottom cut off makes a good 
shade, and a convenient one is made by inverting 
a glass funnel. (See Fig. 26.) 



CURRENT MEASUREMENTS. 75 

The opening at the top is stopped by a cork, 
through which passes a hook from vvhic^ the fibre 
is suspended. 

The needles are caused to vibrate around the 
fibre as an axis by means of a magnet, without 
however, any pendulum motion, and their times of 
vibration noted. This is done by noting the in- 
stant of passage in front of an ink mark on the 
surface of the glass. The mark should be placed 
so that the needle when at rest points to it. 

The time taken for lo swings should be noted, 
then for the next lo, and so on, and the results 
averaged up to give the time for a single oscilla- 
tion. The swings should not be excessive in 
amplitude. Then, taking the length, diameter and 
weight of the magnets in C. G. S. units calculate 
the moment of inertia by the following formula : 

where / = length in centimetres, r = | diameter 
in centimeters and w = weight in grammes. 

Let M = moment of the magnet, i. e.^ the 
strength of one of its poles multiplied by the 



76 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



distance between them, and T = the time in 
seconds of a single vibration, then 

4 7r2 I 



M H 



f 2 



The magnetometer should now be set up in 
front of a scale on which a spot of light is reflected 
from its mirror. The scale should, of course, be at 



Ai: 



I.....I .'!,...! 



6W^6' 




Tlead'ng Scaff- I K— S ■ — -V 

i"i"i"l"'"l"i'T''"l' '",l"'"l"n^ 



© 



I. amp 



T^^^ 



Fig. 27. 

right angles to the line of light when the mirror 
is at rest, and should be a known distance away, 
preferably an even number of its scale divisions, 
say 100. A plan of magnetometer arrangement is 
shown in Fig. 27. 

Place one of the magnets in the cork on the 



CURliENT MEASUREMENTS. 77 

wooden scale as shown, with its middle on a line 
with the magnetometer needle, and observe the 
deflection on the reading scale, which call 5. 
Then letting d equal the distance from the mag- 
netometer mirror to the reading scale, and a^ the 
angle through which the mirror turns, we have 

s 

tan 2 a = - 
d 

from which, with a table of natural tangents, we 
easily find a. We also note this distance L of the 
magnet from the needle, and get the value 

vj from the formula 



/2\ 3 

^2 tana 



/M /2\i 

^ M 

We now have the value M H and JJ' and by 

dividing the first by the second we get the value 
of //2, from which //is easily derived. Knowing 
this, we proceed with our tangent galvanometer. 
This is a galvanometer consisting of a coil of wire, 
whose dimensions are accurately known, which 
acts upon a needle at its centre. The tangent of 
the deflection of this needle is proportional to the 
current passing around the coil. If neither the 



78 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

breadth nor the depth of the coil is greater than 
■^Q, the mean diameter of the coil and the needle 
is short in comparison with the diameter, the 
following equation holds true with a very small 

error 

H r 
C = fj tan a 

2 TT H 

where Cis the current passing through the coil in 
C. G. S. units (ten times the practical unit or 
ampere), H is the intensity of the horizontal 
component of the earth's magnetism as given 
above, r is the mean radius of the coil in centi- 
metres, TV the number of turns in the coil, a the 
angle through which the needle turns. The 
diameter and number of turns of each layer of 
wire must be carefully taken as it is wound on, and 
great care used to make the wire lie smoothly and 
evenly and to prevent contacts between the 
adjacent coils. 

The angle may be read off by a beam of light 
reflected from a mirror attached to the needle, upon 
a scale or by a pointer attached to the needle and 
moving over a scale divided into degrees or better, 
tangents. In the latter arrangements the scale 



CURRENT MEASUREMENTS. 79 

from which the readings are taken should be pasted 
on a mirror, and when making an observation the 
eye should be brought into such a position that 
the pointer hides its image, and any error due to 
parallax is avoided. The pointer should be made 
as light as possible to avoid the effects of inertia 
when you wish it to come to rest. A glass tube 
drawn out to a thin straight thread is often used, 
as is also an aluminum wire flattened at the ends 
in a vertical plane. The suspension of the needle 
may be made by means of a jewel resting on a 
hardened steel point as in a compass or by means 
of a silk fibre, the latter preferably, to eliminate 
the error due to friction. It is well to make all 
parts of the galvanometer which can be made so, 
of wood. Brass may and must be used in certain 
places, such as for screws and rigid supports, but 
it is difficult to get it entirely free from iron, and 
this makes it a bad thing to use. Wood is very 
liable to warp out of shape, but if it is perfectly 
dry and is ^' built up " of a number of pieces whose 
grain crosses, this difficulty may be almost entirely 
avoided. 

It is often convenient to vary the range over 



80 ELECTHICAL MEASUREMENTS FOR AMATEURS. 

which the galvanometer may be used by winding 
it with a number of coils of different sized wire. 
A single strip of copper makes a good coil for 
heavy currents. The galvanometer must be set 
up on the spot where the magnetometer measure- 
ments of //^were made, and with the plane of its 
coil in the magnetic meridian. The needle and 
pointer — if a pointer be used — should be at right 
angles to each other, although this is not strictly 
necessary, and the pointer when the current is off 
should stand exactly over zero on the scale. Then 
try if equal currents passed through the galva- 
nometer in opposite directions deflect the pointer 
by equal amounts. If they do not, the galvanome- 
ter coil is not exactly on the magnetic meridian, 
and it must be revolved until it is, the scale being 
shifted at the same time to keep its zero under the 
pointer. 

As the most sensitive point for making a galva- 
nometer reading is at 45°, the current should be 
arranged so as to give about this reading. This 
may often be done by means of shunts when their 
resistance and that of the galvanometer is accu- 



CURRENT MEASUREMENTS. 81 

rately known. When the galvanometer constants 
are not known the value of \ 

H r 

2 TT N 

in the formula may be determined by calibration, 
from some other source. One of the best methods 
for doing this and likewise for calibrating any 
current measuring instrument is by means of the 
copper voltometer. 

The subject has been investigated pretty 
thoroughly and it has been found that with ordinary 
commercial copper sulphate and good water, (not 
necessarily distilled, but such as can usually be 
had from the city mains,) results may be obtained 
which have only a small percentage of error, if 
ordinary care is taken in making the experiments. 
Silver will give more accurate results, but besides 
being very expensive it requires very careful ma- 
nipulation by a trained experimenter. The copper 
sulphate is dissolved in the water until it gives a 
density of from 1.15 to 1.18. The solution should 
give a distinctly acid reaction, and if it does not 
do so when it is first made a few drops of sulphuric 
'acid should be added. The plates are to be made 



82 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



of sheet copper, the thinner the better, that from 
which dynamo brushes are made is very good. For 
currents up to 15 amperes, they should be made 
something as shown in Figure 28. 

The long tongue is to fasten them into a clip 
with, and allows the square part which is to be 



r^ 



f O cen :^ 



I 



Jl. 



Fig. 28. 

plated on to be entirely submerged. The corners 
are all to be carefully rounded and the edges 
smoothed. Great care must be taken after the 
plates are once made ready, not to touch them 
with the fingers as a greasy mark will be left which 
will not be plated on. The preparation of the 
plates is a matter demanding some care. The sur- 



CURRENT MEASUREMENTS. 



face must be scoured bright with sand-paper and 
then washed off in running water, f he plate is 
then placed lightly upon a blotting pad to remove 
the surplus of water, and then dried before a fire 
or over a spirit flame, care being taken that the 
plate doe^ not get sensibly heated. 

If the surface is much oxidized it may be im- 
mersed for a few seconds in strong nitric acid and 
then rinsed off and dried as above. The plates are 
to be held by their tongues by stiff springs, clips 
of brass or platinoid wire, which are attached to a 
wooden frame over the top of the cell. There 
must be a loss plate on each side of each gain 
plate. In cells which have only one gain plate 
there will be two loss plates, and in cells with two 
gain plates there will be three loss plates and so on. 
The plates are to be held rigidly parallel to each 
other and for the size plate mentioned above 
about 15mm. apart. 

The area of the plates is governed by the current 
to be measured. The gain plate may be almost 
anything from 20 sq. cm. per ampere upwards, 
about 50 sq. cm. per ampere is a good ratio. If 
the loss plate area is allowed to get much below 



84 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

40 sq. cm. per ampere the current is apt to 
fluctuate. If the current strength is too great for 
one plate a number of them may be coupled up in 
parallel. It is also a good plan where the current 
is not large to couple up similar voltameters in 
series so that you may check the results obtained 
from one by those from the other.. 

After having placed the plates in the solution 
the current is turned on and adjusted by means of 
a variable resistance in the circuit to some even 
reading on the instrument. This done, stop the 
current and remove the gain plates and quickly 
rinse and dry them. Then weigh them carefully 
and replace them in the bath and turn on the cur- 
rent. Note the time carefully, by a stop watch if 
possible. The current should be nearly right but 
will probably need a little adjustment which should 
be made quickly. The instrument should be care- 
fully watched and any variation in the current 
quickly corrected. 

The current should be left on for about two 
hours, and after carefully noting the time, be turned 
off and the plates quickly removed, carefully 
washed in running water and dried. Then weigh 



CUKRENT MEASUREMENTS. 85 

the gain plates, and from the increase in weight 
calculate the current. One coulomb of electricity 
will deposit .000329 gramme of copper. Hence 
the number of amperes equals the weight of 
copper deposited, divided by the number of 
seconds, times .000329. 

The gain plate should have a bright flesh col- 
ored appearance, and if it has not there is some- 
thing wrong with the solution or the current 
strength. There is sometimes a tendency for the 
deposit to become rough and granular about the 
edges of the plate. In case it does, care must be 
taken not to lose any of it in washing. This ten- 
dency however generally indicates too great cur- 
rent strength, and may be corrected by proper 
attention to this detail. 

Larger currents will in general, require special 
arrangements of plates, clips, etc., which may be 
left to the ingenuity of the reader. We will briefly 
describe the principles of a few commercial instru- 
ments, and close our chapter on current measure- 
ments. 

Many, if not most of the instruments used for 
current measurements, can be adapted to potential 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



measurements by a change in the winding so that 
many things will be said here which will not need 
repetition in the next chapter. The Ayrton & 
Perry spring ammeter and voltmeter, consists of a 
vertical solenoid, which sucks into its middle a 
light piece of soft iron. (See Fig. 29.) 

This iron is attached to the lower end of a 
spring, made of a flat strip of phosphor bronze and 




Fig. 29. 

which when extended causes a large rotary move- 
ment of the free end. The other end is attached 
to a milled head on the top of the instrument by 
which the pointer is adjusted to zero. 

A small compass in one corner of the base in- 
dicates the direction of flow of the current. This 
instrument is not graduated along the lower part 
of the scale, as the core does not become fully 



CURRENT MEASUREMENTS. 



87 



saturated with small currents, and hence does not 
give a very sure indication. Another ammeter on 
a somewhat similar principle is made by surround- 
ing a tube containing water with a coil, the current 
in which acts upon a piece of iron in a sort of 
hydrometer floating in the water. (See Fig. 30.) 
The iron is high enough out of the coil so that 




Fig. 30. 

it is pulled down as the current increases, and the 
indications are read off like those of an hydrometer. 

A number of instruments depend upon the re- 
pulsion of two similarly magnetized pieces of soft 
iron. (See Fig. 31.) 

The two pieces are enclosed in the same coil of 
wire, one of them being fixed and the other hung 



88 ELECTKICAL MEASUBEMENTS FOR AMATEUJIS. 

from a pivot to which is also attached the pointer. 
When the current passes, the north and south 
poles of each are opposite the same poles on the 
other, and consequently exert a repulsion, which 
is arranged so as to work the pointer and which is 
in general balanced by gravity. These instru- 
ments, and to some extent all instruments 
which depend at all upon the magnetization of 




Fig. 31. 

soft iron, suffer somewhat from the effects of per- 
sistent magnetism, that is to say, the readings are 
not always the same with a rising current as with 
a falling current, as after the iron has been highly 
magnetized and the current gradually lowered the 
magnetism is retained and does not fall until the 
current has been greatly reduced. This can some- 
times be helped by tapping the instrument lightly, 
(which is a bad thing to do if the instrument is 



CURllENT MEASUREMENTS. 



89 



jewelled,) or by opening the current before taking 
a reading, if a voltmeter, or short circuiting the in- 
strument if an ammeter. You then get all your 
readings on a rising current, the way in which the 
instrument was probably calibrated. 




Jl 



Fig. ^2. 



An instrument made by the General Electric 
Company, is shown in Fig. 32. 

The current is led around in a circular ring 
which is nearly enclosed on three sides by a stirrup 
of thin iron. This stirrup is suspended from a 



90 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

pivot which is a little to the left of the centre of 
the ring, so that when the pointer travels across 
the scale the stirrup approaches the ring. When 
the current is turned on the iron stirrup, according 
to the well known law, tries to shorten the lines 
of force around the ring as much as possible, and 
in order to do this it moves up closer to the ring 
and thus moves the pointer. 

The peculiar shape to the '-' fin " on the ring is 
for the purpose of making a proper spacing of the 
division marks on the scale. 

There are a number of instruments working 
on the galvanometer principle, that is, they 
have a magnetic needle which tends to set 
itself at right angles to a coil carrying a cur- 
rent. Some of these have an artificial and some a 
natural magnetic field to balance the effect of 
the coil, and some have a spring. The artificial 
field may be produced either by a permanent or 
electro-magnet. The former is better adapted for 
voltmeters than the latter, since it takes too much 
current to saturate the magnets and increases the 
liability to a heating error. This heating error, by 
the way, is one which is only introduced into volt- 



CUKRENT MEASUREMENTS. 91 

meters. An increase of the temperature of the 
wire due to the current passing or to local causes 
increases the resistance of the wire and thus re- 
duces the current of a voltmeter and makes it read 
wrong. In an ammeter all the current has to 
pass through its coils, so the heating effect is not 
important. For this reason, then, the electro- 
magnetic field is not so bad for ammeters, although 
even then there is a chance for persistent mag- 
netism errors, and the possibility that if the mag- 
nets get overheated it may change their suscep- 
tibilty. 

Permanent magnets are frowned upon in many 
quarters on account of their liability to change. If 
however, they are properly made in the first place 
and are *'aged" after magnetizing, by being boiled 
in water and roughly handled and jarred, they will 
be pretty constant. An instrument of this sort 
must be very carefully handled and not jolted or 
jarred, or brought near any other strong magnets 
such as dynamo fields, but with proper care it will 
remain quite constant. It should however be 
frequently checked to see what change there is 



92 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

in it. A notable example of this kind of instru- 
ment is the Thomson graded galvanometer. 

This is a galvanometer made with the usual coil 
of wire and needle, the latter being pivoted on a 
jewel and having a long aluminum pointer. The 
box containing the needle may be slid along the 
axis of the coil, and marks are made upon the base 
board by which to locate the box. By bringing 
the box nearer to or farther away from the coil it 
is possible to get a great range of readings. 
Attached to the compass box is a semi-circular 
magnet which makes the controlling field, and the 
strength of the magnet is marked upon it. 

Siemens makes a neat little galvanometer with 
a long vertical coil and a little bell magnet sus- 
pended within it. 

The turning of the magn et is balan ced by a spring 
attached to a milled head by which the magnet is 
brought back to its zero position. 

It is used for measuring only small currents 
and has a resistance box to go in series with 
it, by which it may be made to measure potentials. 
It is rather too sensitive to external influences 
to be of much use outside of a laboratory. 



CURRENT MEASUREMENTS. 



93 



The d'Arsonval instrument is a very satisfactory 
one to work with. It consists of a permanent mag- 
netic field, within which is suspended a movable coil 
through which the current passes. By properly 
shaping the pole pieces of the permanent magnet 
and the core inside the coil, a scale can be obtained 
in which the divisions are nearly equal. 




Fig. 33. 

The Weston ammeters and voltmeters are made 
on this principle. The movement of the coil is 
balanced by a spring through which the current 
is led to the coil. This necessarily limits the 
amount of current which may be taken into the 
coil, and renders it necessary where large currents 
are to be measured, to use a low resistance and 
attach the ends of the coil to the ends of the re- 



94 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

sistance. For measuring high potentials a resist- 
ance is introduced in series with the coil. It is 
thus possible with a little shifting of connections, 



Fig. 34. 
to make the same instrument serve for both am- 
meter and voltmeter. (See Fig. 33.) 

The Siemens dynamometer is a very useful and 
accurate instrument for current measurement. 
(See Fig. 34.) 



CUKRENT MEASUKEMENTS. 95 

It consists of two approximately rectangular 
coils, whose planes are at right angles to each other 
and with their centre lines coincident. One coil is 
fixed and the other is suspended from a fibre and 
is controlled by a spring attached to a milled head. 
The ends of the wire of the movable coil dip into 
mercury cups for the current. 

The current is sent in series through the two 
coils and their tendency is to place themselves in 
the same plane. This tendency is resisted by the 
spring, and by the aid of the milled head the mov- 
able coil is brought back to its initial position. 
The distance through which the milled head is 
turned is shown by a pointer, and is a measure of 
the force acting on the coil. This force is propor- 
tional to the product of the currents in the two 
coils, since these currents are identical to the 
square of the current. A printed table accom- 
panies each instrument, giving the value in amperes 
for different deflections. 

This instrument has the advantage which few 
others have of being applicable to the measure- 
ment of alternating currents, as the direction of 
the current has no effect on the direction in which 



\ 



96 ELECTBICAL MEASUREMENTS FOB AMATEURS. 

the movable coil turns, and there is no iron mag- 
net about it. 

A special form of this instrument is called the 
wattmeter. It is the same as the other with the 
exception that one coil is wound with fine wire. 
The instrument is used to determine the energy- 
consumed by a piece of electrical apparatus, by 




giving the product of the potential by the current 
going through it. The fine wire coil is connected 
in parallel with the apparatus, and the thick wire 
in series with it. The force tending to turn the 
movable coil is then proportional to the products 
of the two currents, which are themselves propor- 
tional to the current and potential of the appara- 
tus, and we thus get a reading proportional to the 
watts consumed. 



CURRENT MEASUREMENTS. 



97 



Lord Kelvin's electric balances are upon a 
somewhat similar principle. They have a mov- 
able coil between, and parallel to two other coils 
which are stationary. The current is sent through 
all three in such a way that the movable coil is 
attracted by one of the stationary coils and re- 
pelled by the other. The movable coil is attached 




Fig. 36. 

to one arm of a balance, and there is a similar 
system of coils on the other arm. (See Fig. 35.) 
The adjustments are made by shifting a little 
slider along the balance arm until balance is ob- 
tained, and the current is then known from the 
position of the slider. To reduce friction to a 
minimum and still secure a free passage for the 
electricity into the movable coils, the balance arm is 



98 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

suspended by a number of very fine copper wires. 
Their cross section is not great, but their super- 
ficial area is so great that they readily radiate the 
heat generated by the current. (See Fig. 36.) 



POTENTIAL MEASUREMENT. 99 



CHAPTER IV. 

POTENTIAL MEASUREMENT. 

The primary standard for potential measure- 
ments nowadays is generally the standard cell. 
This cell is constructed with great care, and gives 
under certain conditions, an E. M. F. which is 
nearly constant. A brief description will be given 
of two forms and the method of using them. 

The standard Daniell cell, as its name indicates, 
is one whose elements are copper and zinc in a 
liquid composed of zinc and copper sulphates. 
There are a number of forms of this cell, one of the 
best being made as shown in Fig. 37. 

It is a U shaped glass tube with a stop cock in 
one side near the bottom. The elements are a 
copper and a zinc rod which pass through rubber 
stoppers in the ends of the tube and are connected 
to the wires outside. These rods are of the purest 
metal obtainable, the copper rod being made by 
plating thickly upon a copper wire, and the zinc 
rod is made of redistilled zinc and is amalgamated 



100 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



with pure mercury. The solutions are pure zinc 
and copper sulphates and are nearly saturated, 
although the matter of density is not important so 
long as it does not vary much from the above and 
is the same for both liquids. 

The zinc sulphate is first poured in until it 




Fig. ^']. 
Stands a little above the stop cock opening, and 
then both liquids are poured together, zinc sulphate 
in the right hand tube and copper sulphate in the 
left hand. This must be done as gently as possible 
in order that they may not mix, and the tube is 
canted to the right side occasionally until the line 
of separation of the liquids is opposite the cock 



POTENTIAL MEASUREMENT. 



101 



and the mixed liquids drawn off until the line is 
distinct. The copper must be perfectly clean on 
its surface and show no signs of oxidation. The 
E. M. F. is about i.i true volt at ordinary tem- 
peratures. 




Fig. 38. 

Fresh liquid should be used every time as the 
E. M. F. varies considerably with different solu- 
tions. A feeble current should be allowed to pass 
through it before using, to give a fresh coat of 
copper to the copper element. The cell will not 



102 ELECTEICAL MEASUREMENTS FOR AMATEURS. 

polarize perceptibly, if the resistance in the ex- 
ternal circuit is above 7000 ohms. 

A form of the Latimer Clark cell is shown in 
Fig. 38. 

A small test tube is used for the cell. A plati- 
num wire is passed in at the bottom and sealed for 
one of the terminals. Pure mercury is poured in- 
to the bottom of the tube and covers the platinum 
wire and forms one of the plates. Above this is 
a paste of mercurous sulphate and zinc carbonate. 
In this paste is a rod of zinc, which is connected 
by a gutta-percha covered wire to the outside of 
the cell. 

Lord Rayleigh's description of the method of 
charging the cell is as follows : '' Pour in sufficient 
mercury to cover the platinum wire sealed through 
the bottom of the tube. The best mercury for the 
purpose is that which has been distilled in vacuo. 
The paste should next be introduced, care being 
taken not to soil the sides above the proper level. 
To prepare this paste it is first necessary to 
make a solution of zinc sulphate. Mix in a flask, 
distilled water with about twice its weight of 
crystals of pure zinc sulphate, and add a little pure 



POTENTIAL MEASUREMENT. 103 

zinc carbonate to neutralize the free acid. Effect 
the solution \^\\h gentle heat. Allow the mixture 
to stand to precipitate any iron that may be 
present. Filter the solution in a warm place into 
a stock bottle. When it is intended for use, ex- 
pose the solution to a gentle heat for some time and 
draw off the solution from near the crystals at the 
bottom of the bottle, in order that there may be cer- 
tainty of the solution being saturated. To pre- 
pare the paste, rub together in a mortar 150 gram- 
mes of pure mercurous sulphate, 5 grammes of zinc 
carbonate, and as much of the saturated zinc sul- 
phate as is required to make a thick paste. [Care 
should be taken to get mercuroiis and not mercuric 
sulphate. The former is white, while the latter 
may be detected by its turning yellow on the ad- 
dition of water.] It is best to leave the paste in a 
mortar for two or three days, rubbing it at intervals 
with additions of zinc sulphate until all carbonic 
anhydrite has disappeared. The paste should then 
be transferred to a well stoppered bottle, where it 
should be kept for several months. Before pour- 
ing out for use the bottle should be well shaken. 
The zincs are cut from rods sold as redistilled 



104 ELKCTRICAL MEASUREMEl^TTS FOR AMATEURS. 

zinc. A copper wire insulated with gutta-percha, 
should be soldered to the top of each zinc, after 
which the zinc should be cleaned by dipping it in 
sulphuric acid, and then washed with distilled 
water and dried with filtering paper. To support 
the zinc centrally in the tube, it is passed through 
a ring of cork (nicked to allow the escape of air) 
that just fits within the tube. The cork is pushed 
down until its lower surface nearly touches the 
paste, in order that as much air as possible may be 
excluded. Above the cork a layer of marine glue 
should be poured in order to seal the cell.'' 

A cell thus made, if used on only very weak 
currents, never short circuited and not exposed to 
large variations of temperature, will have an E. M. 
F. given by the formula, 

E=i.435 {i —.00077 (t — 15)} 
where E is the E. M. F. in true volts, and / the 
temperature in degrees centigrade. 

The Daniell cell may be used to compare the E. 
M. F. of another cell or a battery by the following 
arrangement. (See Fig. 39.) 

S represents the standard cell, B the cell or 
battery whose E. M. F. is to be measured, G a 



POTENTIAL MEASUREMENT. 



105 



sensitive galvanometer with a key, and Ri, R^ re- 
sistances which may be varied. These resistances 
should be high in order to reduce the current to a 
minimum, and are adjusted until the galvanometer 
is not deflected upon closing its key. Under these 
circumstances, letting r^ and r^ represent the re- 



fl m 



\ R' \ n^ ) 

WNAA/ ' vAAAA/^ ^ 

Fig. 39. 

sistances respectively of the cell under test and 
the standard, and E^ and E^ their E. M. F's we 
have the equation 

^1 = Ri+^i 

By making another adjustment and finding a 
new set of values for the adjustable resistances, 
which call R^ R^ we have 

El ^ Rg + ri 
E2 R4 + r^ 



106 ELECTKICAL MEASUEEMENTS FOR AMATEUKS. 

By combining the two equations to eliminate r^ 
and ^2 which are supposed unknown, we get 

^2 R2 R4 

from which we easily get the value of E^. 

If the resistances R^ and R^ are made large 
enough to be so that the battery resistances are 
negligible, but one measurement will be necessary 
which will give the equation 

?i = ?Li . •. E = ^2 ^i 
E2 R2 R2 

This method may be applied to calibrating a 
potential galvanometer by replacing the resistance 
R-^ by it. 

In using the Clark's cell, it is necessary that 
only an infinitesimal current be used, and Poggen- 
dorf devised a method in which when balance is 
obtained, the current from the standard cell is 
null. 

In Figure 40 a battery B supplies the current 
which passes over the resistances R^ and R^ ; the 
standard is connected as indicated in series with a 
galvanometer, a key and a high resistance, the 



POTENTIAL MEASUREMENT. 



107 



latter for the purpose of preventing a dangerously 
high current from passing through the standard in 
case of accident. E^ equals the battery E. M. F. 
around the two known resistances R^ and i?2 ^^^d 



^llllil 

B 



— AAAAAn 



L0.. 



Fig. 40. 



-^AAAAr- J 



E^ the E. M. F. of the standard cell, then if when 
the key is depressed 

El Ri H" R 2 

E2 R2 

the potential around i?2 due to the current passing 
over it will be the same as that due to the stand- 
ard cell, and there will be no current through the 
galvanometer. A wire when arranged like that of 
a slide wire bridge, may be used instead of the two 
resistances, and if of uniform resistance throughout, 
the drop of potential between any two points on it 
will be proportional to the length included between 
them. 



108 



ELECTRICAL MEASUREMENTS FOR AMATEURS. 



By measuring the length between the terminals 
of a standard cell which has been applied to the 
wire as above, and forming a proportion between 
this length and that between the terminals of a 
cell whose E. M. F. is desired under similar cir- 
cumstances, we get the ratio between the E. M. 
F. of the standard and the unknown cell. 

The same arrangement may be used as shown 




Fig. 41. 

in Figure 41 for calibrating voltmeters. The volt- 
meter terminals are applied so as to include 
the standard cell between them, and when the 
adjustments are made so that no current passes 
through the standard cell circuit, the potentials 
around the cell and around the voltmeter are pro- 
portional to the lengths or resistances of the wire 
included between them. The practical application 



POTENTIAL MEASUREMENT. 



109 



of this method to voltmeter calibration, may be 
made by means of a Wheatstone's Bridge box of 
coils. 

The connections are made as shown in the dia- 
gram, (See Fig. 42,) where 5 is the standard cell, 
G a sensitive galvanometer, V, M. the voltmeter 



illllh 

B 







K^ 






Fig. 42. 

to be tested, R^ an adjustable resistance to re- 
gulate the current from the battery B, R^ ?i resist- 
ance equal to theE.M.F. of the standard multiplied 
by 100 if the voltmeter is to be tested in the neigh- 
borhood of 100 volts. (For a temperature of 20° C, 
this would be nearly 142.9 ohms.) R^ a resistance 
which when added to R3 will make an even 



110 ELECTEICAL MEASUREMENTS FOR AMATEURS. 

number, say 200 ohms, (in the above instance this 
would be 57.1 ohms.) 

Pull out all the plugs in the ratio arm of the 
bridge between the middle and the point at which 
i?3 is connected and make the resistance of the 
rheostat arm such that when added to R^ -\- R^ 
the result will be the number of volts desired on 
the voltmeter multiplied by 100. For 50 volts this 
would be 4800 ohms. 

Then touching down the key marked K.,^, adjust 
R^ until upon tapping K^ the deflection of the 
galvanometer G is very small, then make a final 
adjustment of R^ using K^ instead of K^* The 
idea in using Kcy^ is to keep a large resistance in 
series with the standard cell to prevent a danger- 
ous current passing over it, until the first rough 
adjustment of R^ is made. The main objection to 
this method given by Mr. Swinburn, who describes 
it, is that as we get to higher potentials it puts a 
large strain on the coils in the box, which being 
wound with doubled wires have their starting and 
finishing ends close together. The writer how- 
ever has used this method a number of times 
without damaging his resistance box and believes 



POTENTIAL MEASUREMENT. 



Ill 



that most of them are made well enough to stand 
the test. The battery is made of storage cells, 
which, as they are required for potential mainly 
and need give only a small current, may be made 
quite srnall. 



CM^O 



MLZTn 




Fig. 43. 

A convenient cell may be made up of small 
glass tumblers and sheet lead, cut and bent into 
the form shown. (See Fig. 43.) 

They are placed in the glasses so that the inside 
plate in one cell becomes the outside plate in the 
next, and are kept from touching by three or four 



112 ELECTEICAL MEASUKEMENTS FOR AMATEURS. 

small wedges between the plates in each cell. The 
liquid is sulphuric acid and water mixed beforehand 
and allowed to cool. Its specific gravity should be 
1 1 70. A little non-evaporating oil poured over the 
surface of the liquid in each cell will prevent loss 
of this liquid by spraying. 

The cells should be charged from a dynamo, in 
parallel if there is not the E. M. F. to do it in 
series, for a few hours in one direction and then 
discharged, and charged for a few hours in the other 
direction and again discharged. This is repeated 
four or five times, when the cells will be ready for 
use. 

A more convenient way of getting the E. M. F. 
for calibrating, if a dynamo is available, is to use the 
dynamo and separately excite the fields. By put- 
ting an adjustable resistance in the field circuit of 
the dynamo you can get a very convenient adjust- 
ment. This is especially convenient when large 
numbers of voltmeters are to be compared with a 
standard. For use with the standard cell it would 
be well to wind a number of resistance coils to take 
the place of the resistance box, if there is any like- 
lihood of there being enough testing to justify the 



POTENTIAL MEASUEEMENT. 113 

outlay. You would thus save your bridge from 
possible damage and could make up the few coils 
required into a more portable form. 

The voltmeter can be calibrated of course by 
comparison with a standard galvanometer which 
measures currents. If the galvanometer is wound 
so that it will measure currents as small as the 
voltmeter uses, they may be placed in series and 
the current measured, and the potential calculated 
from the voltmeter resistance, taken at its working 
temperature. Or, if the galvanometer measures 
only large currents, put it in series with a known 
resistance at each end of which the voltmeter ter- 
minals are placed, and we get the potential from 
the formula 

E = C ^^ 
R + r 

where E is the potential on the voltmeter, Cthe 
current measured by the galvanometer, R the volt- 
meter resistance and r the shunt resistance. (See 
Fig. 44.) 

Another method of making potential measure- 
ments is by means of the quadrant electrometer, 
which depends upon the attraction exerted upon 



114 



ELECTBICAL MEASUREMENTS FOR AMATEURS. 



each other by two adjacent metal plates which are 
charged at different potentials. It will not be de- 
scribed here however, as the electrometer is an 
expensive instrument and requires expert ma- 
nipulation to give satisfactory results. 

We will close the chapter with the description 
of a few instruments specially adapted for potential 
measurement. The electrostatic voltmeter of 



B 



O-^ 



r 
(WW\A 



Fig. 44. 



Lord Kelvin depends upon the electrometer prin- 
ciple just mentioned, of the attraction of two 
electrified plates. (See Fig. 45.) 

The movable plate is suspended on knife edges 
between two vertical stationary plates, and has a 
pointer attached to it which passes over the scale 
above. When the inside and outside plates are 
oppositely electrified, the inside plate is drawn in 



POTENTIAL MEASUREMENT. 



115 



between the other two increasing its capacity as a 
condenser at the same time. The value of the 
scale division is changed by hanging a little weight 
to the lower end of the movable plate, one division 
on the scale having a range of from 50 volts to 200 
volts by changing the weights. 




Fig. 45. 

As a matter of safety the electrical connection 
between the terminals of the instrument and the 
plates is made through a fine copper wire enclosed 
in a U shaped glass tube. The wire will fuse 
should any short circuit occur, and the long passage 
through the tube will prevent the formation of an 
arc. This instrument is of course applicable to 
the measurement of the potential of alternating 



116 ELECTRICAL MEASUREMENTS FOR AMATEURS. 

currents as well as that of direct currents. The 
same instrument in a somewhat different form, is 
the multicellular voltmeter, which may be used for 
potentials from 40 to 800 volts. 

The movable plate instead of working in a ver- 
tical plane, works horizontally and is suspended 
by a platinum wire from" a milled torsion head, by 
which the pointer is adjusted to zero. Instead of 
being composed of but one vane however, the 
movable plate is made up of a number of them, 
each working between two fixed plates. A needle 
attached to the spindle, on which the vanes are 
fastened, moves over a scale which reads directly 
in volts. 

The Cardew voltmeter is an instrument which 
depends upon the expansion of a fine wire heated 
by the passage of a current over it. 

Figure 46 shows diagramatically the arrange- 
ment of the instrument. The fine wire is attached 
rigidly at a and b to the frame of the instrument 
and runs over the ivory pulleys at P, P^ P, 

Pulleys P, P^ are fastened to the end of a tube 
through which the wires pass, and pulley P, is 
fastened to a wire which passes around a wheel W 



POTENTIAL MEASUEEMENT. 



117 



and is then attached to a spring 5 which keeps 
everything taut. Of course any movement of the 
wire will cause the wheel W to turn, and this 
through a small gear and pinion magnifies the 
motion and transmits it to the pointer. 

The frame which connects the pulleys Fy P, 
with the rest of the instrument is made of rods 
composed of steel and brass in such proportions, 




Fig. 46. 

that they have the same temperature coefficient of 
expansion as the wire, and the instrument will thus 
come to zero when both are at the same tempera- 
ture. The majority of the other instruments used 
in potential measurement are identical in principle 
with those used in current measurement, and as 
the most important of these has been referred to 
there, they need not be mentioned again here. 




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Chapter 2.— Forms of Armatures. 

Chapter 3. — Drum Winding. 

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Chapter 0. — General Methods of Winding. 

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Chapter S. — Dynamos. 

Chapter 9. — Motors. 



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